In nautilus and Unity the external drive has a nice short descriptive name "mcat", but all partitions on the 4 internal drives are displayed as a size (834 GB filesystem) or a huge 32-character string form of a GUID:

I'm guessing the external drive is nice, short, sweet and readable because that drive may have no partitions (well, just one I guess) and that name may be the drive label, whereas partitions usually don't have names. That may explain my problem, but doesn't solve it.

Is there some way to give reasonable names to these partitions in nautilus and Unity?

Partition labelling is possible using the GParted tool. You just select the partition you want to change the label to, right click and choose the label option. However, you can't change the label for mounted partitions, so you are out of luck for your system partitions.